Previous article Next article New Consequences of Kolmogorov’s Formula for Infinitely Divisible LawsE. B. BagirovE. B. Bagirovhttps://doi.org/10.1137/1136011PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] B. V. Gnedenko and , A. N. Kolmogorov, Limit distributions for sums of independent random variables, Addison-Wesley Publishing Company, Inc., Cambridge, Mass., 1954ix+264 16,52d 0056.36001 Google Scholar[2] Fritz Oberhettinger, Fourier transforms of distributions and their inverses, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1973ix+167, A Collection of Tables 50:5373 0306.65002 Google Scholar[3] E. T. Whittaker and , G. N. Watson, A Course in Modern Analysis, Cambridge University Press, Cambridge, 1952 Google Scholar[4] A. P. Prudnikov, , Yu. A. Brychkov and , O. I. Marichev, Integrals and Series. Elementary Functions, Nauka, Moscow, 1981, (In Russian.) 0511.00044 Google Scholar[5] I. S. Gradshtein and , I. S. Ryzhik, Tables of Integrals, Series and Products, Academic Press, New York, 1965 Google Scholar[6] V. M. Zolotarev, One-dimensional stable distributions, Translations of Mathematical Monographs, Vol. 65, American Mathematical Society, Providence, RI, 1986x+284 87k:60002 0589.60015 CrossrefGoogle Scholar[7] G. Bateman and , A. Erdeljy, Higher Transcendental Functions, Vol. 1, McGraw-Hill, New York, 1953 Google Scholar[8] E. Lukacs, Characteristic Functions, Griffin, London, 1972 Google Scholar[9] William Feller, An introduction to probability theory and its applications. Vol. I, Third edition, John Wiley & Sons Inc., New York, 1968xviii+509 37:3604 0155.23101 Google Scholar[10] Douglas Kelker, Infinite divisibility and variance mixtures of the normal distribution., Ann. Math. Statist., 42 (1971), 802–808 44:3415 0234.60009 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails An Estimate of the Total Variation of Signed Measures Arising in Connection with the Central Limit TheoremYu. V. ProkhorovTheory of Probability & Its Applications, Vol. 36, No. 2 | 17 July 2006AbstractPDF (219 KB) Volume 36, Issue 1| 1992Theory of Probability & Its Applications1-208 History Submitted:15 April 1989Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1136011Article page range:pp. 138-143ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics